Uncountably many groups of type.

Abstract: We construct uncountably many discrete groups of type F P; in particular we construct groups of type F P that do not embed in any finitely presented group. We compute the ordinary, ℓ 2, and compactly supported cohomology of these groups. For each n ⩾ 4 we construct a closed aspherical n‐manifold that admits an uncountable family of acyclic regular coverings with non‐isomorphic covering groups. [ABSTRACT FROM AUTHOR]